Many transistor-based electronic circuits will function properly only if they are supplied a very precise power-supply voltage; if the supply voltage drifts too far out of an acceptable tolerance, the transistors it powers may function unpredictably, poorly, or not at all. Many factors may affect the value of the supply voltage, including fluctuations in a power source (e.g., a battery or AC mains supply), changes in temperature, or changes in the load on the power supply. One way that a power supply may maintain a more stable output voltage is to generate a “reference voltage”: a voltage derived from a fixed, stable, and constant value such as (in many transistor-based supplies) the energy bandgap intrinsic to a given material. The energy bandgap of silicon, for example, is approximately 1.11 electron-volts at room temperature, regardless of its power source or loading. Because the energy bandgap is susceptible to changes in temperature, however, a simple reference-voltage generation circuit generates two reference values: a first one that changes in the same direction as a change in the temperature (a so-called proportional-to-absolute-temperature or “PTAT” value) and a second one that changes in the direction opposed to the temperature change (a complementary-to-absolute-temperature or “CTAT” value). The two values are added together and, to first order, the temperature dependencies cancel each other out. FIG. 1A illustrates a simple bandgap-reference circuit 100 that includes a first transistor 102 configured for generating a CTAT value 104 across a first resistor 106 and a second transistor 108 for generating a PTAT value 110 across a second resistor 112. The output value 114 combines the two generated values 104, 110.
As supply voltages have dropped and transistors have become less tolerant of variations, however, the simple bandgap-reference circuit 100 shown in FIG. 1A has proved inadequate in some applications because it does not compensate for second-order effects of temperature on the bandgap value (which are explained in greater detail below). A more sophisticated bandgap-reference circuit 150, shown in FIG. 1B, includes first-order PTAT and CTAT value-generating transistors 152, 154 (analogous to the transistors 102, 108 in the simpler circuit 100 of FIG. 1A) but also includes a third transistor 156 that is configured to generate a second-order temperature factor. The first two transistors 152, 154 generate PTAT and CTAT currents 158, 160 (which are tapped via a buffer 162 and fed back to control current sources 164). A portion of the current 166 generated by the third transistor 156 is subtracted from the PTAT/CTAT currents 158, 160 via resistors 168, 170, thereby accounting for the second-order effects. The output current is mirrored using a current mirror 172, and an output voltage is developed at an output terminal 174 across an output resistor 176.
While the second-order circuit 150 of FIG. 1B improves upon the simpler circuit 100 of FIG. 1A, it is designed based on an approximation of the second-order current 166 that may not always hold true. Specifically, it is assumed that the current 166 generated by the third transistor 156 is not significantly affected by the additional contributions added from the PTAT/CTAT currents 158, 160. In reality, however, this may not always be the case; the third transistor 156 may be calibrated to generate the second-order factor (the “α” factor, as referred to throughout this application) at a particular temperature (for example), but changing conditions may upset the balance of currents flowing into it, producing an error.
Furthermore, the calibration/characterization of the transistors 152, 154, 156 must generally be predetermined by a computer simulation of the circuit 150 because, once manufactured, the circuit 150 cannot be adjusted. The computer model of the transistors 152, 154, 156 may not be accurate enough, however, to precisely determine the value of a process-dependent factor (referred to herein as “XTI” and explained in greater detail below). This XTI parameter may be especially difficult to predict in CMOS processes, in which models of bipolar junction transistors (BJTs) are not well-developed. The actual value of this process-dependent XTI factor (as explained in greater detail below) may thus differ from the simulated or predicted value, further increasing the error of the circuit 150. This error may be unacceptable in some applications; a need therefore exists for an adjustable voltage-reference circuit that correctly and robustly cancels out second-order temperature effects in its generated output.